The majority of literature studies the convergence of stochastic Newton by establishing a high probability error recursion. For example, [1]}, [2]}, [3]}, [4]} all showed (or showed a similar result) that stochastic Newton methods enjoy a local linear-quadratic recursion:
\(\Vert _{t+1}-^\star \Vert  \le c_1\Vert _t - ^\star \Vert  + c_2\Vert _t-^\star \Vert ^2 \quad \quad \text{with probability } 1 - \delta ,\) 
